Search results for: lower approximations

Authors: Michinori Nakata, Hiroshi Sakai

Abstract:

A rough set, which consists of lower and upper approximations, is formulated in information tables containing possibilistic information. First, lower and upper approximations on the basis of possible world semantics in the same way as Lipski did in the field of incomplete databases are shown in order to clarify fundamentals of rough sets under possibilistic information. Possibility and necessity measures are used, as is done in possibilistic databases. As a result, each object has certain and possible membership degrees to lower and upper approximations, which degrees are the lower and upper bounds. Therefore, the degree that the object belongs to lower and upper approximations is expressed by an interval value. And the complementary property linked with the lower and upper approximations holds, as is valid under complete information. Second, the approach based on indiscernibility relations, which is proposed by Dubois and Prade, are extended in three cases. The first case is that objects used to approximate a set of objects are characterized by possibilistic information. The second case is that objects used to approximate a set of objects with possibilistic information are characterized by complete information. The third case is that objects that are characterized by possibilistic information approximate a set of objects with possibilistic information. The extended approach create the same results as the approach based on possible world semantics. This justifies our extension.

Keywords: rough sets, possibilistic information, possible world semantics, indiscernibility relations, lower approximations, upper approximations

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Authors: M. Y. Bakeir

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Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

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Authors: Kajingulu Malandala, Ranganai Edmore

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The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: quantile regression, Delaporte distribution, count data, integrated nested Laplace approximation

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Authors: Serge Provost, Yishan Zang

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Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Hassan J. Al Salman, Ahmed A. Al Ghafli

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In this study, we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed-point theorem to prove existence of the approximations at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

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Authors: Hassan Al Salman, Ahmed Al Ghafli

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In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

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Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

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Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

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Authors: Dongchuan Su, Hai Xie, Naibin Jiang

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Under severe accident cases, the nuclear reactor core may meltdown inside the lower head of the reactor pressure vessel (RPV). Retaining the melt pool inside the RPV is an important strategy of severe accident management. During this process, the inner wall of the lower head will be heated to high temperature of a thousand centigrade, and the outer wall is immersed in a large amount of cooling water. The material of the lower head will have serious creep damage under the high temperature and the temperature difference, and this produces a great threat to the integrity of the RPV. In this paper, the ANSYS program is employed to build the finite element method (FEM) model of the lower head, the creep phenomena is simulated under the severe accident case, the time dependent strain and stress distribution is obtained, the creep damage of the lower head is investigated, the integrity of the RPV is evaluated and the theoretical basis is provided for the optimized design and safety assessment of the RPV.

Keywords: severe accident, lower head of RPV, creep, FEM

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Authors: Po-Jen Su, Huann-Ming Chou

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In this article we uses the residual correction method to deal with transient thermoelastic problems with a hollow spherical region when the continuum medium possesses spherically isotropic thermoelastic properties. Based on linear thermoelastic theory, the equations of hyperbolic heat conduction and thermoelastic motion were combined to establish the thermoelastic dynamic model with consideration of the deformation acceleration effect and non-Fourier effect under the condition of transient thermal shock. The approximate solutions of temperature and displacement distributions are obtained using the residual correction method based on the maximum principle in combination with the finite difference method, making it easier and faster to obtain upper and lower approximations of exact solutions. The proposed method is found to be an effective numerical method with satisfactory accuracy. Moreover, the result shows that the effect of transient thermal shock induced by deformation acceleration is enhanced by non-Fourier heat conduction with increased peak stress. The influence on the stress increases with the thermal relaxation time.

Keywords: maximum principle, non-Fourier heat conduction, residual correction method, thermo-elastic response

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Authors: Esther Liyanage, Indrajith Liyanage, A. A. J. Rajaratne

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During the 30 year civil war in Sri Lanka, a large number of individuals were injured and disabled. These disabilities have reduced their daily physical activities which may cause reduction in flexibility of upper limb, shoulder girdle, lower back and lower limb. Muscle flexibility is important for a healthy lifestyle. The main objective of the study was to assess the upper limb, shoulder girdle and lower back, hamstring flexibility of the intact lower limb in disabled individuals in the North and Eastern parts of Sri Lanka. Back saver sits and reach test and shoulder scratch test described in FITNESS GRAM was used in the study. A total of 125 disabled soldiers with lower limb disabilities were recruited for the study. Flexibility of the lower back and hamstring muscles of uninjured lower limb was measured using back saver sit and reach test described by Wells and Dillon (1952). Upper limb and shoulder girdle flexibility was assessed using shoulder stretch test. Score 0-3 was given according to the ability to reach Superior medial angle of the opposite scapula, top of the head or the mouth. The results indicate that 31 (24.8%) disabled soldiers have lower limb flexibility less than 8, 2 (1.6 % ) have flexibility of 8, 2 (1.6 %) have flexibility of 8.5, 11 ( 8.8% ) have flexibility of 9, 14 (11.2 %) have flexibility of 9.5, 23 (18.4 %) have flexibility of 10, 17 (13.6 %) have 10.5 flexibility, 13 (10.4%) have 11 flexibility, 2 (1.6%) have 11.5 flexibility, 10 (8 %) have flexibility of 12 and 3 (2.34 %) have flexibility of 12.5. Six disabled soldiers (4.8%) have upper limb flexibility of 2 and remaining 95.2% have normal upper limb flexibility (score 3). A reduction in the flexibility of muscles in lower body and lower limbs was seen in 25% disabled soldiers which could be due to reduction in their daily physical activities.

Keywords: disability, flexibility, rehabilitation, quality of life

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Authors: Alina Fedossova, Jose Jorge Sierra Molina

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SIP problems are part of non-classical optimization. There are problems in which the number of variables is finite, and the number of constraints is infinite. These are semi-infinite programming problems. Most algorithms for semi-infinite programming problems reduce the semi-infinite problem to a finite one and solve it by classical methods of linear or nonlinear programming. Typically, any of the constraints or the objective function is nonlinear, so the problem often involves nonlinear programming. An investment portfolio is a set of instruments used to reach the specific purposes of investors. The risk of the entire portfolio may be less than the risks of individual investment of portfolio. For example, we could make an investment of M euros in N shares for a specified period. Let yi> 0, the return on money invested in stock i for each dollar since the end of the period (i = 1, ..., N). The logical goal here is to determine the amount xi to be invested in stock i, i = 1, ..., N, such that we maximize the period at the end of ytx value, where x = (x1, ..., xn) and y = (y1, ..., yn). For us the optimal portfolio means the best portfolio in the ratio "risk-return" to the investor portfolio that meets your goals and risk ways. Therefore, investment goals and risk appetite are the factors that influence the choice of appropriate portfolio of assets. The investment returns are uncertain. Thus we have a semi-infinite programming problem. We solve a semi-infinite optimization problem of portfolio selection using the outer approximations methods. This approach can be considered as a developed Eaves-Zangwill method applying the multi-start technique in all of the iterations for the search of relevant constraints' parameters. The stochastic outer approximations method, successfully applied previously for robotics problems, Chebyshev approximation problems, air pollution and others, is based on the optimal criteria of quasi-optimal functions. As a result we obtain mathematical model and the optimal investment portfolio when yields are not clear from the beginning. Finally, we apply this algorithm to a specific case of a Colombian bank.

Keywords: outer approximation methods, portfolio problem, semi-infinite programming, numerial solution

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Authors: A. Torokhti

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A new method of mathematical modeling of the distributed nonlinear system is developed. The system is represented by a combination of the set of spatially distributed sensors and the fusion center. Its mathematical model is obtained from the iterative procedure that converges to the model which is optimal in the sense of minimizing an associated cost function.

Keywords: mathematical modeling, non-linear system, spatially distributed sensors, fusion center

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Authors: Khawlah Al-Khalidi

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Prevalence of lower third molar impactions and angulations among Yemeni population The purpose of this study was to look into the prevalence of lower third molars in a sample of patients from Ibb University Affiliated Hospital, as well as to study and categorise their position by using Pell and Gregory classification, and to look into a possible correlation between their position and the indication for extraction. Materials and methods: This is a retrospective, observational study in which a sample of 200 patients from Ibb University Affiliated Hospital were studied, including patient record validation and orthopantomography performed in screening appointments in people aged 16 to 21. Results and discussion: Males make up 63% of the sample, while people aged 19 to 20 make up 41.2%. Lower third molars were found in 365 of the 365 instances examined, accounting for 91% of the sample under study. According to Pell and Gregory's categorisation, the most common position is IIB, with 37%, followed by IIA with 21%; less common classes are IIIA, IC, and IIIC, with 1%, 3%, and 3%, respectively. It was feasible to determine that 56% of the lower third molars in the sample were recommended for extraction during the screening consultation. Finally, there are differences in third molar location and angulation. There was, however, a link between the available space for third molar eruption and the need for tooth extraction.

Keywords: lower third molar, extraction, Pell and Gregory classification, lower third molar impaction

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Authors: Brahim Boukabcha, Amar Rebbouh

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The bootstrap method based on the idea of exploiting all the information provided by the initial sample, allows us to study the properties of estimators. In this article we will present a theoretical study on the different methods of bootstrapping and using the technique of re-sampling in statistics inference to calculate the standard error of means of an estimator and determining a confidence interval for an estimated parameter. We apply these methods tested in the regression models and Pareto model, giving the best approximations.

Keywords: bootstrap, error standard, bias, jackknife, mean, median, variance, confidence interval, regression models

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Manik Sharma

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Understanding the anatomy and normal anatomical variations of the lower limb arterial system is undeniably important not only to understand the pathology involving the vessels of the lower limb but also as a part of endovascular intervention and surgical planning in cases that demand them as a part of treatment. There have been very few cases of duplication of SFA cited in the literature, close to six worldwide and this being the seventh case in the world and first to be reported in the Indian population. We incidentally came across this normal variant during US lower limb (US-LL) duplex scan in a patient with claudicating pain in bilateral lower limbs hence suspected of having peripheral vascular disease. It was confirmed on CT-Peripheral Angiography (CT-PA), which was done successively.

Keywords: peripheral vascular disease, claudicating pain, normal anatomical variants, endovascular intervention, duplication, CT-peripheral angiography, duplex scan, Iohexol

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Authors: Leila Ben Haj Said, Sihem Bellagha, Karim Allaf

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The present study deals with the dehydrofreezing assisted by instant controlled pressure drop (DIC) treatment of apple fruits. Samples previously dehydrated until different water contents (200, 100, and 30% dry basis (db)) and DIC treated were frozen at two different freezing velocities (V+ and V-), depending on the thermal resistance established between the freezing airflow and the sample surface. The effects of sample water content (W) and freezing velocity (V) on freezing curves and characteristics, exudate water (EW) and texture variation were examined. Lower sample water content implied higher freezing rates, lower initial freezing points (IFP), lower practical freezing time (PFT), and lower specific freezing time (SFT). EW (expressed in g exudate water/100 g water in the product) of 200% and 100% db apple samples was approximately 3%, at low freezing velocity (V-). Whereas, it was lower than 0.5% for apple samples with 30% db water content. Moreover, the impact of freezing velocity on EW was significant and very important only for high water content samples. For samples whose water content was lower than 100% db, firmness (maximum puncture force) was as higher as the water content was lower, without any insignificant impact of freezing velocity.

Keywords: dehydrofreezing, instant controlled pressure drop DIC, freezing time, texture

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Authors: Neda Valizadeh, Mani Mofidi, Sama Haghighi, Ali Hashemaghaee, Soudabeh Shafiee Ardestani

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Background: There are many systems and parameters to evaluate trauma patients in the emergency department. Most of these evaluations are to distinguish patients with worse conditions so that the care systems have a better prediction of condition for a better care-giving. The purpose of this study is to determine the relationship between axillary body temperature and mortality in patients hospitalized in the intensive care unit (ICU) with multiple traumas and with other clinical and para-clinical factors. Methods: All patients between 16 and 75 years old with multiple traumas who were admitted into Emergency Department then hospitalized in the ICU were included in our study. An axillary temperature in the first and the second day of admission, Glasgow cola scale (GCS), systolic blood pressure, Serum glucose levels, and white blood cell counts of all patients at the admission day were recorded and their relationship with mortality were analyzed by SPSS software with suitable statistical tests. Results: Axillary body temperatures in the first and second day were statistically lower in expired traumatic patients (p=0.001 and p<0,001 respectively). Patients with lower GCS had a significantly lower first-day temperature and a significantly higher mortality. (p=0.006 and p=0.006 respectively). Furthermore, the first-day axillary temperature was significantly lower in patients with a lower first-day systolic blood pressure (p=0.014). Conclusion: Our results showed that lower axillary body temperature in the first day is associated with higher mortality, lower GCS, and lower systolic blood pressure. Thus, this could be used as a predictor of mortality in evaluation of traumatic patients in emergency settings.

Keywords: fever, trauma, mortality, emergency

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: Xin Li, Zhenxue Jiang, Zhuo Li

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Generally, shale gas is trapped within shale systems with low porosity and ultralow permeability as free and adsorbing states. Its production is controlled by properties, in terms of occurrence phases, gas contents, and percolation characteristics. These properties are all influenced by porous features. In this paper, porosity differences of marine shales were explored between Lower Cambrian shale and Lower Silurian shale of Sichuan Basin, South China. Both the two shales were marine shales with abundant oil-prone kerogen and rich siliceous minerals. Whereas Lower Cambrian shale (3.56% Ro) possessed a higher thermal degree than that of Lower Silurian shale (2.31% Ro). Samples were measured by a combination of organic-chemistry geology measurement, organic matter (OM) isolation, X-ray diffraction (XRD), N2 adsorption, and focused ion beam milling and scanning electron microscopy (FIB-SEM). Lower Cambrian shale presented relatively low pore properties, with averaging 0.008ml/g pore volume (PV), averaging 7.99m²/g pore surface area (PSA) and averaging 5.94nm average pore diameter (APD). Lower Silurian shale showed as relatively high pore properties, with averaging 0.015ml/g PV, averaging 10.53m²/g PSA and averaging 18.60nm APD. Additionally, fractal analysis indicated that the two shales presented discrepant pore morphologies, mainly caused by differences in the combination of pore types between the two shales. More specifically, OM-hosted pores with pin-hole shape and dissolved pores with dead-end openings were the main types in Lower Cambrian shale, while OM-hosted pore with a cellular structure was the main type in Lower Silurian shale. Moreover, porous characteristics of isolated OM suggested that OM of Lower Silurian shale was more capable than that of Lower Cambrian shale in the aspect of pore contribution. PV of isolated OM in Lower Silurian shale was almost 6.6 times higher than that in Lower Cambrian shale, and PSA of isolated OM in Lower Silurian shale was almost 4.3 times higher than that in Lower Cambrian shale. However, no apparent differences existed among samples with various matrix compositions. At late diagenetic or metamorphic epoch, extensive diagenesis overprints the effects of minerals on pore properties and OM plays the dominant role in pore developments. Hence, differences of porous features between the two marine shales highlight the effect of diagenetic degree on OM-hosted pore development. Consequently, distinctive pore characteristics may be caused by the different degrees of diagenetic evolution, even with similar matrix basics.

Keywords: marine shale, lower Cambrian, lower Silurian, om isolation, pore properties, om-hosted pore

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Authors: Gubhinder Kundhi, Paul Rilstone

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It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. Finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: bootstrap, Instrumental Variable, Edgeworth expansions, Saddlepoint expansions

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Authors: Juan Sepúlveda

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Energy is a fundamental component in sustainability, the access and use of this resource is related with economic growth, social improvements, and environmental impacts. In this sense, energy efficiency has been studied as a factor that enhances the positive impacts of energy in communities; however, the implementation of efficiency requires strong policy and strategies that usually rely on individual measures focused in independent dimensions. In this paper, the problem of energy efficiency as a multi-objective problem is studied, using scientometric analysis to discover trends and patterns that allow to identify the main variables and study approximations related with a further development of models to integrate energy efficiency and MCA into policy making for small communities.

Keywords: energy efficiency, MCA, scientometric, trends

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Authors: Abubaker A. Yousif, Muhamad S. Yasir

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The Effectiveness of lower doses of high-LET radiations is not accurately determined by using energy-based physical parameters such as absorbed dose and radio-sensitivity parameters. Therefore, an attempt has been carried out in this research to propose alternative parameter that capable to quantify the effectiveness of these high LET radiations at lower doses regions. The linear energy transfer and mean free path are employed to achieve this objective. A new mathematical form of the effectiveness of high-LET radiations at lower doses region has been formulated. Based on this parameter, the optimized effectiveness of high-LET radiations occurs when the energy of charged particles is deposited at spacing of 2 nm for primary ionization.

Keywords: effectiveness, low dose, radiation mean free path, linear energy transfer

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Authors: Albena Ivanova, Jill Kurp, Austin Hampe

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Cereal products in the US contain rich information on the front of the package (FOP) as well as point-of-purchase (POP) summaries provided by the store. These summaries frequently are confusing and misleading to the consumer. This study explores the relationship between perceived quality, objective quality, price, and value in the cold cereal industry. A total of 270 cold cereal products were analyzed and the price, quality and value for different summaries were compared using ANOVA tests. The results provide evidence that the United States Department of Agriculture Organic FOP/POP are related to higher objective quality, higher price, but not to a higher value. Whole grain FOP/POP related to a higher objective quality, lower or similar price, and higher value. Heart-healthy POP related to higher objective quality, similar price, and higher value. Gluten-free FOP/POP related to lower objective quality, higher price, and lower value. Kid's cereals were of lower objective quality, same price, and lower value compared to family and adult markets. The findings point to a disturbing tendency of companies to continue to produce lower quality products for the kids’ market, pricing them the same as high-quality products. The paper outlines strategies that marketers and policymakers can utilize to contribute to the increased objective quality and value of breakfast cereal products in the United States.

Keywords: cereals, certifications, front-of-package claims, consumer health.

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Authors: Madina Hamiane

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Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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